15.14.24 problem 24

Internal problem ID [3196]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 24
Date solved : Sunday, March 30, 2025 at 01:20:58 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=\sin \left (3 x \right )+x \,{\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 39

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-6*diff(diff(diff(y(x),x),x),x)+9*diff(diff(y(x),x),x) = sin(3*x)+x*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (3 c_1 x -2 c_1 +3 c_2 \right ) {\mathrm e}^{3 x}}{27}-\frac {\cos \left (3 x \right )}{162}+\frac {\left (-1+x \right ) {\mathrm e}^{x}}{4}+c_3 x +c_4 \]

✓ Mathematica. Time used: 1.127 (sec). Leaf size: 52

ode=D[y[x],{x,4}]-6*D[y[x],{x,3}]+9*D[y[x],{x,2}]==Sin[3*x]+x*Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{4} e^x (x-1)-\frac {1}{162} \cos (3 x)+\frac {1}{27} e^{3 x} (c_2 (3 x-2)+3 c_1)+c_4 x+c_3 \]

✓ Sympy. Time used: 0.156 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*exp(x) - sin(3*x) + 9*Derivative(y(x), (x, 2)) - 6*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{4} e^{3 x} + x \left (C_{2} + C_{3} e^{3 x} + \frac {e^{x}}{4}\right ) - \frac {e^{x}}{4} - \frac {\cos {\left (3 x \right )}}{162} \]